{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7.3. Getting started with Bayesian methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as st\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def posterior(n, h, q):\n",
    "    return (n + 1) * st.binom(n, q).pmf(h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 100\n",
    "h = 61\n",
    "q = np.linspace(0., 1., 1000)\n",
    "d = posterior(n, h, q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "podoc": {
     "output_text": "Posterior distribution"
    }
   },
   "outputs": [
    {
     "data": {
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cK6+8Eps3b06QBgCA5qSEAwAAAEpSihVfKUqvlPbee+/YZ599Ms1Yt25dTJ06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\npKZNm1rO2bZtm5YvX25gIgAA4G6UcAAAAAAAjxozZ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2fPhwUxpwku74PLWcavPmzYZxLy8vjRw50pQ5EhMTFRUVZUou/M/dd99tGD9x4oSL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\nAAAAAAAAADDZ/wNF6dHhKq3DygAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "Posterior distribution"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(q, d, '-k')\n",
    "ax.set_xlabel('q parameter')\n",
    "ax.set_ylabel('Posterior distribution')\n",
    "ax.set_ylim(0, d.max() + 1)"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 2
}
